# How do you differentiate f(x)=tan(e^(x-x^2))  using the chain rule?

Jun 17, 2018

$f ' \left(x\right) = {e}^{x - {x}^{2}} \cdot \left(1 - 2 x\right) \cdot {\sec}^{2} \left({e}^{x - {x}^{2}}\right)$

#### Explanation:

Note that

$\left(\tan \left(x\right)\right) ' = {\sec}^{2} \left(x\right)$
so we get by the chain rule

${\sec}^{2} \left({e}^{x - {x}^{2}}\right) \cdot {e}^{x - {x}^{2}} \cdot \left(1 - 2 x\right)$